Ally Points can be received through any battle (10 each for using a non-friend as support, 25 for using a friend, and 100 points for using a given AI support), Login Incentives, or Event Quests' event shops.

For the last stage of limit breaking, you can obtain this by completing Character Quests.
Owner Medallions also have a small chance of dropping from both Advanced (40 stamina) ELEMENT Limit Break and WEAPON TYPE Limit Break daily quests. It's unknown which of these quests has the higher chance of dropping one, if there's any difference at all.